Method for Determining Hydraulic Pressure Parameters in a Displacement Pump

ABSTRACT

The invention relates to a method for determining hydraulic parameters in a displacement pump, wherein the displacement pump has a movable displacement element, which bounds the metering chamber, which is connected to a suction and pressure line by means of valves, wherein a drive is provided for the oscillating motion of the displacement element. In order that pumped fluid can be alternately sucked into the metering chamber via the suction line and pressed from the metering chamber via the pressure line by means of an oscillating motion of the displacement element, a physical model having hydraulic parameters according to the invention is established for the hydraulic system, the force exerted by the displacement element on the fluid located in the metering chamber or the pressure in the metering chamber is determined and the position of the displacement element is determined, and at least one hydraulic parameter is calculated by means of an optimization calculation

The present invention relates to a method for determining hydraulic parameters in a displacement pump. The displacement pump has a movable displacement element, which bounds the metering chamber, which is connected to a suction and pressure line via valves, with the result that pumped fluid can be alternately sucked into the metering chamber via the suction line and pressed out of the metering chamber via the pressure line by means of an oscillating motion of the displacement element. Displacement pumps additionally have a drive for the oscillating motion of the displacement element.

There are, for example, electromagnetically driven diaphragm pumps, in which the displacement element is a diaphragm, which can be moved backwards and forwards between two extreme positions, wherein in the first extreme position the volume of the metering chamber is at a minimum, while in the second extreme position the volume of the metering chamber is at a maximum. Therefore, if the diaphragm is moved from its first position into the second position, the pressure in the metering chamber will fall, with the result that pumped fluid is sucked into the metering chamber via the suction line. In the case of the movement back, i.e. the motion from the second position into the first position, the connection to the suction line is closed, the pressure of the pumped fluid will increase because of the reducing volume in the metering chamber, with the result that the valve to the pressure line is opened and the pumped fluid is transported into the pressure line. Through the oscillating motion of the diaphragm, on an alternating basis pumped fluid is sucked from the suction line into the metering chamber, and pumped fluid is sucked out of the metering chamber, and pumped fluid is conveyed from the metering chamber into the pressure line. The flow of pumped fluid into the pressure line is also called the metering profile. This metering profile is essentially determined by the motion profile of the displacement element.

In the case of electromagnetically driven diaphragm pumps, the diaphragm is connected to a thrust member, which is usually mounted pretensioned in a spring-loaded manner at least partially within an electromagnet. As long as the electromagnet does not have a current flowing through it, with the result that no magnetic flux is built up inside it, the spring-loaded pretensioning ensures that the thrust member and thus the diaphragm remains in a predetermined position, e.g. the second position, i.e. the position at which the metering chamber has the greatest volume. If a current is now impressed on the electromagnet, a magnetic flux forms, which brings the correspondingly formed thrust member inside the electromagnet from its second position into the first position, which causes the pumped fluid located in the metering chamber to be conveyed from the metering chamber into the pressure line.

Upon activation of the electromagnet, there is an essentially abrupt stroke of the metering piece and thus of the metering diaphragm from the second into the first position.

Typically, such electromagnetically driven diaphragm pumps are used if the fluid volume to be metered is significantly greater than the metering chamber volume, with the result that the metering rate is essentially determined by the frequency, or the timing, of the current flow through the electromagnet. If, for example, the metering rate is doubled, at the same time a current temporarily flows through the electromagnet twice as frequently, which in turn results in the motion cycle of the diaphragm being shortened and taking place twice as frequently.

Such a magnetic metering pump is described in EP 1 757 809, for example.

However, the use of this magnetic metering pump reaches its limits when only low metering rates are necessary, with the result that the abrupt metering of an entire stroke is not desirable.

In the named EP 1 757 809, it is therefore already proposed to provide a position sensor with which the position of the thrust member, or the diaphragm connected thereto, can be determined. By comparing the actual position of the thrust member with a predetermined target position of the thrust member a control of the motion can then take place, with the result that magnetic metering pumps can also be used to convey significantly lower fluid amounts, as the stroke motion no longer takes place abruptly, but rather in a controlled manner.

In practice it is difficult to find suitable control parameters. In fact, different control parameters are determined empirically in each case for different thrust member position states and stored in a memory, with the result that the pump can retrieve and use the corresponding control parameters in dependence on the position of the thrust member.

However, it is very laborious to determine the control parameters. In addition, it depends heavily on the circumstances in the metering chamber, such as e.g. the density and the viscosity of the pumped fluid. The control therefore only functions satisfactorily when the system approximately corresponds to the desired state. In particular when there are pressure fluctuations on the suction and/or pressure line, when cavitation occurs, when air accumulates in the metering chamber or when there are changes in the viscosity of the pumped fluid, the control parameters stored in the memory are unsuitable and the control accuracy decreases, with the result that the actual metering profile differs significantly from the desired metering profile. However, this is undesirable in particular in the case of continuous metering of very small amounts, such as e.g. in the case of the chlorination of drinking water.

The control accuracy can, for example, be improved by measuring the density and/or viscosity of the pumped fluid and using the measurement result to select the control parameters.

However, for such a measurement at least one additional sensor is necessary, which would increase the selling price of the displacement pump and additionally needs maintenance and repair. Density and viscosity changes have therefore hitherto not been taken into account in the control.

Starting from the described state of the art, the object of the present invention is therefore to provide a method that allows hydraulic parameters to be determined, such as e.g. the density or the viscosity of the pumped fluid, without additional sensors being required.

This is achieved according to the invention in that a physical model having hydraulic parameters is constructed for the hydraulic system, the force exerted by the displacement element on the fluid located in the metering chamber or the pressure in the metering chamber and the position of the displacement element is determined, and at least one hydraulic parameter is calculated by means of an optimization calculation.

By hydraulic parameters is meant any parameter of the hydraulic system—except the position of the displacement element—which influences the flow of the pumped fluid through the metering chamber.

Hydraulic parameters are thus e.g. the density of the pumped fluid in the metering chamber as well as the viscosity of the fluid in the metering chamber. Further hydraulic parameters are, for example, the hose or pipe length and diameter of hoses and pipes which are at least at times connected to the metering chamber.

The required determination of the position of the displacement element can take place via the position sensor which is usually present in any case. The speed and acceleration of the displacement element can be determined from the position of the displacement element.

If the method according to the invention is used in an electromagnetically driven metering pump, and best of all in an electromagnetically driven diaphragm pump, in a preferred embodiment the current through the electromagnetic drive can be measured and the force exerted by the displacement element on the fluid located in the metering chamber is determined from the measured current and the measured position of the displacement element. In this case, a separate pressure sensor is not necessary. However, the present method can, of course, also be used with a separate pressure sensor.

It is an inherent property of the displacement pump that the hydraulic system always changes significantly when one of the valves via which the metering chamber is connected to the suction and pressure line is opened or closed.

It is easiest to model the system for the case in which the valve to the suction line is open and the valve to the pressure line is closed. Namely, a flexible hose which ends in a storage tank at ambient pressure is usually mounted on the valve to the suction line.

This situation exists during the so-called suction stroke i.e. while the displacement element is moving from the second position into the first position. This hydraulic system could, for example, be described by means of the nonlinear Navier-Stokes equation taking into account laminar and turbulent flows. In addition to the density and the viscosity of the pumped fluid, the diameter of the hose which connects the suction valve to the storage tank, the length of the hose and the height difference which the fluid in the hose must negotiate are also to be considered as hydraulic parameters.

Depending on the system used, further meaningful assumptions can be made. By means of an optimization calculation, which can, for example, take place via the known gradient method or Levenberg-Marquardt algorithms, it is possible to determine the hydraulic parameters contained in the physical model which best describe the pressure progression in the metering head and the motion, or the speed and acceleration determined therefrom, of the thrust member.

By an optimization calculation is meant any calculation with which the optimal parameters of the system are discovered. Optimal parameters are the parameters which best describe the system, i.e. for which the difference between the model and the measured situation is at a minimum.

The determination method according to the invention could essentially take place simply through a repeated analysis of the suction stroke behavior.

Alternatively, however, the physical model of the hydraulic system can also be considered for the case that the valve to the suction line is closed and the valve to the pressure line is open. As, however, the pump manufacturer as a rule does not know at first in what environment the metering pump is used, and therefore also does not know the pipe system attached to the pressure valve which connects the pressure line to the metering chamber, only a generalized assumption can be made here. Without knowledge of the pipeline system attached to the pressure valve, the constructed physical model can therefore not be constructed as accurately as is the case in the described simplest form for the hydraulic system during the suction stroke.

In a particularly preferred embodiment, physical models for both described hydraulics systems are used and then the valve opening time points are measured or determined and the respectively appropriate physical model is selected in dependence on the result of the determination of the valve opening time points. Essentially, the method according to the invention is then carried out separately for the suction stroke and the pressure stroke. In both cases, values are obtained for the hydraulic parameters, such as e.g. the density and the viscosity of the pumped fluid, which do not correspond exactly in practice. In principle it would therefore be possible to take the average of the different values, wherein it must possibly be taken into account that because of the better description of the actual situation by the physical model during the suction stroke, the value obtained during the suction stroke is weighted more heavily in the averaging than the value ascertained during the pressure stroke.

Of course, there are also application cases in which the hydraulics system is also more complex during the suction stroke.

After the hydraulic parameters have been determined in the manner according to the invention, the constructed physical model can be used with the hydraulic parameters determined in this way in order to determine, for its part, the pressure in the metering chamber.

This knowledge can, in turn, be used to improve the motion control of the thrust member. In a preferred embodiment it is provided that a model-based control, in particular a nonlinear model-based control is used for the drive of the displacement element.

In the case of a model-based control, a model of the process dynamics which is as complete as possible is developed. Using this model it is then possible, put simply, to make a prediction for where the system variables will move to in the next moment.

From this model, a suitable manipulated variable can then also be calculated. A characterizing feature of such a model-based control is thus the constant calculation of the necessary manipulated variables on the basis of measured variables using the system variables given by the model.

Essentially, the underlying physical system is described approximately mathematically by the modeling. This mathematical description is then used to calculate the manipulated variable on the basis of the obtained measured variables. Unlike the known metering profile optimization methods, the drive is thus no longer seen as a “black box”. Instead, the known physical relationships are used to determine the manipulated variable.

By this means, a significantly better control quality can be achieved.

In a preferred embodiment, the position of the displacement element and the current through the electromagnetic drive are measured and a state-space model is used for the model-based control, which uses the position of the displacement element and the current through the magnetic coil of the electromagnetic drive as measured variables.

In a particularly preferred embodiment, the state-space model does not have any further measured variables to be detected, i.e. the model is developed such that it makes a prediction for the immediately following motion of the thrust member solely on the basis of the detected thrust member position and the detected current through the magnetic coil.

In a preferred embodiment, the determined hydraulic parameters are used.

By a state-space model is usually meant the physical description of a present system state. For example, the state variables can describe the energy content of the energy storage elements contained in the system.

For example, a differential equation of the displacement element can be used as model for the model-based control. For example, the differential equation can be an equation of motion. By an equation of motion is meant a mathematical equation which describes the spatial and temporal motion of the displacement element under the effect of external influences. In a preferred embodiment, displacement pump-specific forces which act on the thrust member are modeled in the equation of motion. Thus, for instance, the force exerted on the thrust member by a spring, or the spring constant k thereof, and/or the magnetic force exerted on the thrust member by the magnetic drive can be modeled. The force exerted on the thrust member by the pumped fluid can then be treated as a disturbance variable. In a particularly preferred embodiment, this disturbance variable can then likewise be modeled using the determined hydraulic parameters.

By means of such a state-space model, when the measurement variables are detected, a prediction for the immediately following system behavior can be made.

If the immediately following behavior forecast in this way deviates from the desired predetermined behavior, the system is influenced in a corrective manner.

In order to calculate what a suitable exertion of influence looks like, in the same model the influence of the available manipulated variables on the controlled variable can be simulated. Using known optimization methods, the control strategy which is best at that time can then be selected adaptively. Alternatively, it is also possible to determine a control strategy once on the basis of the model and to then apply this in dependence on the detected measured variables.

In a preferred embodiment, a nonlinear state-space model is therefore chosen as state-space model and the nonlinear control takes place either via control-Lyapunov functions, via flatness-based control methods with flatness-based feedforward control, via integrator backstepping methods, via sliding mode methods or via predictive control. Nonlinear control via control-Lyapunov functions is preferred.

All five methods are known from the field of mathematics and are therefore not explained in more detail here.

Control-Lyapunov functions are, for example, a generalized description of Lyapunov functions. Appropriately chosen control-Lyapunov functions lead to a stable behavior in the framework of the model.

In other words, a correction function is calculated which leads to a stable solution for the model in the underlying model.

In general, there are a large number of control possibilities which lead to the difference between the actual profile and the target profile in the underlying model becoming smaller.

In a preferred embodiment, the model which forms the basis of the model-based control is used to formulate an optimization problem, in which, as a secondary condition for optimization, the electric voltage in the electric motor and thus the energy fed to the metering pump is as small as possible, but at the same time it is achieved that the actual profile approaches the target profile as quickly as possible and with as little overshooting as possible. Moreover, it can be advantageous if the measured signals are filtered using a low-pass filter before the processing in the underlying model in order to reduce the influence of noise.

In a further particularly preferred embodiment it is provided that during a suction-pressure cycle the difference between the detected actual position profile of the displacement element and a desired target position profile of the displacement element is detected and a target position profile which corresponds to the desired target position profile reduced by the difference is used for the next suction-pressure cycle.

Essentially, a self-learning system is realized here. Although the model-based control according to the invention has already led to a significant improvement in the control behavior, there can still be deviations between the target profile and the actual profile. In particular, this cannot be avoided in the case of energy-minimizing selection of the control intervention. In order to reduce this deviation further at least for subsequent cycles, the deviation during a cycle is detected and in the next cycle the detected deviation is at least partially subtracted from the desired target position profile.

In other words, a subsequent pressure-suction cycle is deliberately provided with a “false” target value profile, wherein the “false” target value profile is calculated from the knowledge obtained in the preceding cycle. Namely, if in the subsequent suction-pressure cycle there is exactly the same deviation between actual and target profile as in the previous cycle, the use of the “false” target value profile leads to the actual desired target value profile being achieved as a result.

Although it is essentially possible, and also sufficient in some applications because of the periodic behavior of the system, to carry out the described self-learning steps only once, i.e. to measure the difference in the first cycle and from the second and in all further cycles to correct the target value profile correspondingly, it is particularly preferred if the difference between actual and target profile is determined at regular intervals, best of all in every cycle, and is taken into account correspondingly in the subsequent cycle.

Of course, it is also possible to only use a fraction of the detected difference as profile correction for the subsequent cycle or cycles. This can be advantageous in particular in the cases in which the detected difference is very large, in order not to generate instability in the system by the sudden change in target value.

Furthermore, it is possible to determine the size of the fraction of the detected difference, which is used as profile correction, using the present difference between target and actual profile.

It is also possible that the difference between actual and target profile is measured over several cycles, e.g. 2, and from this an average difference is calculated, which is then at least partially subtracted from the target profile of the subsequent cycles.

In a further alternative embodiment any of the functions dependent on the detected difference can be used for correcting the next target position profile.

In a further preferred embodiment, the modeling according to the invention can be used in order to determine a physical variable in the displacement pump. Thus, for example, the fluid pressure in the metering chamber can be determined.

The equation of motion of the displacement element takes into account all forces which act on the displacement element. In addition to the force applied to the displacement element by the drive, this is also the counterforce applied to the diaphragm and thus to the displacement element by the fluid pressure in the metering chamber.

Thus, if the force applied to the displacement element by the drive is known, conclusions can be drawn from the position of the displacement element, or from the speed or acceleration of the displacement element which can be derived therefrom, about the fluid pressure in the metering head.

For example, if the actual fluid pressure reaches or exceeds a predetermined maximum value, a warning signal can be emitted and the warning signal can be sent to an automatic shutoff, which shuts off the metering pump in response to the warning signal being received. Therefore, if for any reason a valve does not open or the pressure on the pressure line increases sharply, this can be ascertained by the method according to the invention without using a pressure sensor and the pump can be shut off as a precaution. Essentially, the displacement element, with the associated drive, additionally takes over the function of the pressure sensor.

In a further preferred embodiment of the method, a target fluid pressure curve, a target position curve of the displacement element and/or the target current progression through the electromagnetic drive is stored for a motion cycle of the displacement element. The actual fluid pressure can be compared with the target fluid pressure, the actual position of the displacement element with the target position of the displacement element and/or the actual current through the electromagnetic drive with a target current through the electromagnetic drive and, if the differences between actual and target value satisfy a predetermined criterion, a warning signal can be emitted.

The idea that forms the basis of this method step is that certain events, such as for example gas bubbles in the hydraulics system or cavitation in the pump head bring about a recognizable change in the fluid pressure to be expected, and conclusions can therefore be drawn about the named events from the determination of the fluid pressure.

The warning signal can, for example, activate an optical indicator or an audible alarm. As an alternative or in combination therewith, the warning signal can, however, also be directly made available to a control unit, which takes the appropriate measures in response to the warning signal being received.

In the most simple case, the difference of the actual and target value is determined for one or more of the measured, or determined, variables, and if one of the differences exceeds a predetermined value a warning signal is emitted.

However, in order to not only detect the possible error events, such as e.g. gas bubbles in the metering chamber or the occurrence of cavitation, but also to distinguish between them, it is possible to define an individual criterion for each error event.

In a preferred embodiment, a weighted sum of the relative deviations from the target value can be determined and the criterion can be chosen such that a warning signal is emitted if the weighted sum exceeds a predetermined value.

Different weighting coefficients can be assigned to the different error events. In the ideal case, precisely one criterion is satisfied when an error event occurs, with the result that the error event can be diagnosed.

Using the described method it is therefore possible to determine the pressure in the metering head without resorting to a pressure sensor, and from the pressure determined in this way, conclusions can be drawn about certain states in the metering head, which can then in turn trigger the introduction of certain measures.

With the method according to the invention, changes in pressure can be determined very precisely.

In a further embodiment the temporal gradient of a measured or determined variable is therefore ascertained and, if this exceeds a predetermined threshold value, the valve opening or valve closing is diagnosed.

In an alternative embodiment, the mass m of the displacement element, the spring constant k of the spring which pretensions the displacement element, the damping d and/or the electrical resistance R_(Cu) of the electromagnetic drive is determined as physical variable.

In a particularly preferred embodiment, all of the named variables are actually determined. This can take place, for example, by a minimization calculation. All of the named variables, with the exception of the pressure in the metering chamber, represent constants which can be determined by experiment and which as a rule do not change during the operation of the pump. Nevertheless, symptoms of fatigue of the different elements can occur which change the value of the constants. For example, the measured pressure-path progression can be compared with an expected pressure-path progression. The difference of both gradients integrated over a cycle can be minimized by varying the constant variables. If e.g. it is established that the spring constant has changed, a defective spring can be diagnosed.

Such a minimization could also be carried out in the unpressurized state, i.e. when there is no fluid in the metering chamber.

Further advantages, features and application possibilities of the present invention are made clear using the following description of a preferred embodiment and the associated figures. There are shown in:

FIG. 1 a schematic representation of the suction line attached to the displacement pump,

FIGS. 2a-2e example of hydraulic parameters and the time-dependent development thereof,

FIG. 3 a schematic representation of an ideal motion profile,

FIG. 4 a schematic representation of the self-learning function,

FIG. 5 a schematic representation of a pressure-path diagram and a path-time diagram for the normal state and

FIG. 6 a schematic representation of a pressure-path diagram and a path-time diagram for a state with gas bubbles in the metering chamber.

Through the design of a physical model, in particular a nonlinear system description of the hydraulic process in the metering chamber, or in the line connected to the metering chamber, of an electromagnetic metering pump system, it is possible to use model-based identification methods in real time. For this, the hydraulic parameters, i.e. the state variables of the hydraulic models, are evaluated and the system dynamics and the parameters of the hydraulic process are determined.

The position of the displacement element, or the speed and acceleration of the displacement element determined therefrom, and the pressure in the metering chamber which can be determined via the force exerted on the pumped fluid by the diaphragm serve as measured variables, or external variables to be determined.

Because, as a rule, in the named displacement pumps the suction line consists of a hose which connects the suction valve to a storage tank, for the suction stroke, i.e. while the pressure valve is closed and the suction valve is open, the hydraulic system can be described in a simplified manner, as is represented in FIG. 1. The suction line consists of a hose with the diameter D_(S) and the hose length L. The hose bridges a height difference Z.

The nonlinear Navier-Stokes equations can be simplified if it is assumed that the suction line has a constant diameter and is not expandable and that an incompressible fluid is used.

Using known optimization methods, such as e.g. the gradient method or the Levenberg-Marquardt algorithms, the hydraulic parameters are now determined which can best describe the measured position of the thrust member and the measured or determined pressure in the metering chamber using the constructed model as a basis.

In the FIGS. 2a to 2e here, using the example of glycerol as pumped fluid, in each case a hydraulic parameter (dotted line) as well as the values resulting from the method according to the invention (continuous line) are represented over time.

Thus, for example, FIG. 2a shows the density of the pumped fluid. This is approximately 1260 kg/m³ (dotted line). It can be seen that the method according to the invention is able to determine the density within approximately 100 seconds. Although at the time point where t=0 seconds the determined value is still clearly below the actual value, the continuous optimization results in the value for the density determined by the method according to the invention approaching the true value very rapidly (continuous line).

The same is true for the hose length L (see FIG. 2b ), the height difference Z (see FIG. 2c ), the hose diameter (see FIG. 2d ) and the viscosity (see FIG. 2e ).

The parameters determined by the method according to the invention can then, in turn, be used together with the constructed physical model to determine the force exerted on the thrust member by the hydraulic system.

This information can be used for the control. In particular when model-based nonlinear control strategies are used for the control of the motion of the thrust member, the model developed here can physically model the effect of the hydraulic system and take this into account in the form of a disturbance variable feedforward.

The method according to the invention has been developed in connection with a magnetic metering pump. In a preferred embodiment, such a magnetic metering pump has a movable thrust member with a connecting rod firmly connected thereto. The thrust member is mounted to be axially movable in the longitudinal axis in a magnetic casing which is firmly anchored into the pump housing, with the result that when the magnetic coil in the magnetic casing is electrically triggered, the thrust member with connecting rod is drawn into a hole of the magnetic casing against the action of a pressure spring, and after the magnet is deactivated the thrust member travels back into the starting position by means of the pressure spring. The result of this is that when the magnetic coil is continuously activated and deactivated, the thrust member and a diaphragm actuated by this carries out an oscillating motion, which, in the metering head arranged in the longitudinal axis, in cooperation with an outlet and inlet valve leads to a pumping stroke (pressure stroke) and an intake stroke (suction stroke). The activation of the magnetic coil takes place by a voltage being applied to the magnetic coil. The motion of the thrust member can thus be established by the temporal progression of the voltage on the magnetic coil.

It is understood that the pressure stroke and the suction stroke do not necessarily have to last for the same amount of time. On the contrary, as no metering occurs during the suction stroke, but rather the metering chamber is merely filled again with pumped fluid, it is advantageous to carry out the suction stroke as quickly as possible in each case, wherein care is nevertheless to be taken there is no cavitation in the pressure chamber.

On the other hand, the pressure stroke can last a very long time, in particular in application cases in which only very small fluid amounts are to be metered. This results in the thrust member moving only gradually in the direction of the metering chamber. In order to achieve a motion of the thrust member as is represented in an idealized manner in FIG. 3, the motion of the thrust member must be controlled. Only the position of the thrust member and the size of the current through the magnetic coil are customarily available as measured variables.

According to the invention, a (nonlinear) model is therefore developed, which describes the state of the magnetic system.

The following model results for a preferred embodiment:

$\overset{.}{x} = {\begin{bmatrix} \overset{.}{x} \\ \overset{¨}{x} \\ \overset{.}{\Phi} \end{bmatrix} = \begin{bmatrix} \overset{.}{x} \\ {\frac{1}{m}\left( {{{- d}\overset{.}{x}} - {kx} - F_{vor} + F_{p} + {{K_{L}(\delta)}\Phi^{2}}} \right)} \\ {\frac{1}{N_{1}}\left( {{{- R_{cu}}\; \frac{R_{m_{ges}}\left( {\delta,\Phi} \right)}{N_{1}}\Phi} + u} \right)} \end{bmatrix}}$

wherein

m: mass of the thrust member

Φ: magnetic flux

K_(L)(δ)Φ²: magnetic force

N₁: number of turns

u: voltage

d: damping

k: spring constant

F_(var): force on thrust member through spring pretensioning

F_(P): force on thrust member through fluid pressure in conveying chamber

R_(m) _(gec) (δ, Φ): magnetic resistance

R_(Cu): ohmic resistance of the coil

x: position of the thrust member

δ: size of gap between anchor and magnet

This is a nonlinear differential equation system which allows a prediction to be made about the immediately following behavior of the system, starting from a starting point.

Using this model, it is therefore possible to identify future or actually already existing deviations between the target curve and the actual curve. In addition, the model can be used in order to calculate the likely effect of a control intervention.

Because of the measurement of the strength of the current and the position of the thrust member, it is determined in real time how the system is likely to develop. It can additionally be calculated through which control intervention, i.e. through which changes in voltage on the magnetic coil, the system can be moved back into the desired direction.

Of course, there are a large number of possibilities to intervene in the system in terms of control. At every time point, stable solutions for the dynamical system can thus be sought. This calculation step is constantly, i.e. as frequently as the available calculation power allows, repeated in order to obtain an optimal control.

In the case of the model proposed here, it is generally not necessary to determine new stable solutions for the dynamical system at every time point. As a rule it is sufficient to determine the suitable correction function in dependence on the measured variables, i.e. in dependence on the position of the thrust member and the voltage on the magnetic drive, once and to use this the correction function from then on for the control.

Despite this control, there will inevitably be deviations between the target and actual value, as the chosen model always represents an idealization. In addition, the detected measured variables always contain errors (noise).

In order to further reduce the difference between actual and target profile, this difference is measured during a pressure-suction cycle and the sum of the measured difference and the desired target profile is used as target profile for the subsequent cycle. In other words, the fact that the pressure-stroke cycle repeats is utilized. In the subsequent cycle a target value profile which differs from the actual desired target value profile is thus specified.

This self-controlling principle is represented schematically in FIG. 4 for the purpose of clarification. The position of the thrust member is represented on the y-axis and the time is represented on the x-axis.

In the first cycle, a target profile used for the control is represented with a dashed line. This target profile corresponds to the desired target profile which is modeled as a reference profile for comparison in the third cycle. Despite the model-based control according to the invention, the actual profile will deviate from the target profile. In the first cycle of FIG. 4, an actual profile is therefore represented by way of example with a continuous line. For clarification, the deviations between actual and target profile are represented in a more pronounced manner than they occur in practice.

In the second cycle, the difference between the actual profile of the first cycle and the reference profile is then subtracted from the target profile used for the first cycle and the difference is used as target profile for the control during the second cycle. The thus-obtained target profile is represented dashed in the second cycle.

Ideally, in the second cycle the actual profile deviates from the target profile used to the same extent as was observed in the first cycle. This results in an actual profile (drawn in with a continuous line in the second cycle) which corresponds to the reference profile.

By measuring the position of the thrust member and the current through the magnetic drive, F_(P), i.e. the force on the thrust member through the fluid pressure in the conveying chamber, is the only unknown variable. Using this model, the force on the thrust member through the fluid pressure in the conveying chamber can therefore be determined. As the surface area of the thrust member to which the fluid pressure is applied is known, the fluid pressure can be calculated from the force.

Through the described design of a nonlinear system description of the electromagnetic metering pump system, it is possible to use model-based diagnosis methods. For this, the state variables of the system models are evaluated and the pressure in the pump head of the electromagnetic metering pump is determined. The necessary current and position sensors here are already built in the pump system for the purposes of control technology, with the result that the information is already available without the construction of the metering pump needing to be supplemented. Using the temporal change in the state variables and the pressure in the metering head of the pump, the diagnosis algorithms can then be performed.

Thus, for example, the model-based diagnosis of excess pressure in the process and the automated pump switch-off can be realized.

The valve opening and valve closing time points can, for example, be identified via the determination and evaluation of temporal gradients of coupled state variables of the system model. It can be detected when the state gradients overshoot or fall short by means of predetermined limits, which leads to the identification of the valve opening and valve closing time points.

As an alternative, the pressure can also be determined in dependence on the position of the thrust member and the valve opening and valve closing time points can be derived from an evaluation. A corresponding pressure-path diagram is represented on the left in FIG. 5. The associated path-time diagram is represented on the right in FIG. 5. The path-time diagram shows the time-dependent motion of the thrust member. It can be seen that the thrust member first moves forwards from a starting position 1 (x=0 mm) and the volume of the metering chamber decreases (pressure phase). At time point 3, the thrust member passes through a maximum and then moves back into the starting position (suction phase).

The corresponding pressure-path diagram is shown on the left in FIG. 5. It will proceed in the clockwise direction, starting at the coordinate origin at which the thrust member is located in the position 1. During the pressure phase, the pressure in the metering chamber will first increase sharply until the pressure is able to open the valve to the pressure line. Once the pressure valve is open, the pressure in the metering chamber remains essentially constant. The opening point is indicated with the reference number 2. From this time point, which is also recorded on the right in FIG. 5, a metering takes place. With each further motion of the thrust member, metering fluid is pumped into the pressure line. Once the thrust member has reached the maximum position (time point 3), the motion of the thrust member reverses, the pressure valve closes immediately and the pressure in the metering chamber drops again. Once a minimum pressure is reached (time point 4), the suction valve which connects the metering chamber to the suction line opens, and metering fluid is sucked into the metering chamber until the starting position is reached again.

The valve closing time points can be determined from the path-time diagram, as they lie at the displacement maxima of the thrust member. The time points 2 and 4, i.e. the valve opening time points are not as easy to determine, especially as in practice the pressure-path diagram has rounded “corners”. Starting from position 1 in the pressure-path diagram, for example, when 90% of the pressure maximum is reached (known from position 3), the path can therefore be read off and the increase of the pressure-path diagram between points 1 and 2 can be determined. The 90% curve is drawn in dotted. The straight line resulting from this intersects the curve p=p_(max) at the valve opening time point. The time point 4 can also be determined in the same manner. This determination can take place in each cycle and the result used for a later cycle. Changes in the opening time points can thereby also be detected.

By a comparison of the target and actual trajectories of the individual state variables of the system models, gas bubbles in the hydraulics system, cavitation in the pump head of the metering unit and/or valve opening and valve closing time points of the metering units can be diagnosed. In particular when a predetermined error limit is exceeded between the target and actual trajectories, this can trigger a warning signal and corresponding measures.

An example is shown in FIG. 6. Here too, the pressure-path diagram is represented on the left and the path-time diagram is represented on the right. The right-hand figure is identical to the corresponding diagram of FIG. 5. If there are gas bubbles in the hydraulics system which are compressible, that will lead to the pressure valve only opening at time point 2′ and the suction valve only opening at time point 4′. A clear shift in the valve opening time points can thus be used to diagnose the state “air in the metering chamber”. In the case of cavitation, only the valve opening time point 4′ shifts and not the valve opening time point 2, with the result that such a behavior can be used to diagnose the state “cavitation”.

Through the analysis of the individual coupled system state variables, the model-based methodology presented enables an essentially more comprehensive and more valuable diagnosis than has been realized to date.

Moreover, this can be realized with low costs in terms of sensors and high reliability and dependability. Through the higher diagnosis quality, the field of use of electromagnetic metering pump systems can possibly be expanded, as the metering accuracy can now be vastly improved. 

1.-16. (canceled)
 17. A method of determining at least one physical variable in a positive displacement pump, wherein the positive displacement pump has a moveable displacer element delimiting the metering chamber which is connected by way of valves to a suction and a pressure line so that delivery fluid can alternately be sucked into the metering chamber by way of the suction line and urged out of the metering chamber by way of the pressure line by an oscillating movement of the displacer element, wherein there is provided a drive for the oscillating movement of the displacer element, wherein for the displacer element a differential equation is established based on a physical model, at least the position of the displacer element is measured and the physical variable is determined by means of the differential equation, wherein the fluid pressure p of a delivery fluid in a metering chamber of a positive displacement pump is determined as the physical variable, characterized in that if the actual fluid pressure reaches or exceeds a predetermined maximum value a warning signal is output and the warning signal is sent to an automatic shut-down arrangement which shuts down the metering pump in response to reception of the warning signal.
 18. A method of determining at least one physical variable in a positive displacement pump, wherein the positive displacement pump has a moveable displacer element delimiting the metering chamber which is connected by way of valves to a suction and a pressure line so that delivery fluid can alternately be sucked into the metering chamber by way of the suction line and urged out of the metering chamber by way of the pressure line by an oscillating movement of the displacer element, wherein there is provided a drive for the oscillating movement of the displacer element, wherein for the displacer element a differential equation is established based on a physical model, at least the position of the displacer element is measured and the physical variable is determined by means of the differential equation, wherein the fluid pressure p of a delivery fluid in a metering chamber of a positive displacement pump is determined as the physical variable, characterized in that for a movement cycle of the displacer element a target fluid pressure curve, a target position curve of the displacer element and/or the target current pattern through the electromagnetic drive is provided and the actual fluid pressure is compared to the target fluid pressure, the actual position of the displacer element is compared to the target position of the displacer element and/or the actual current through the electromagnetic drive is compared to a target current through the electromagnetic drive and a warning signal is output if the differences between the actual and target values satisfy a predetermined criterion.
 19. A method of determining at least one physical variable in a positive displacement pump, wherein the positive displacement pump has a moveable displacer element delimiting the metering chamber which is connected by way of valves to a suction and a pressure line so that delivery fluid can alternately be sucked into the metering chamber by way of the suction line and urged out of the metering chamber by way of the pressure line by an oscillating movement of the displacer element, wherein there is provided a drive for the oscillating movement of the displacer element, wherein for the displacer element a differential equation is established based on a physical model, at least the position of the displacer element is measured and the physical variable is determined by means of the differential equation, characterized in that the mass m of the displacer element, the spring constant k of the spring prestressing the displacer element, the damping d and/or the electrical resistance R_(Cu) of the electromagnetic drive is determined as the physical variable.
 20. A method as set forth in claim 17, characterized in that the positive displacement pump is an electromagnetically driven metering pump.
 21. A method as set forth in claim 20 characterized in that besides the position of the displacer element the current through the electromagnetic drive is measured and the differential equation uses both the position of the displacer element and also the current through the electromagnetic drive as measurement variables, wherein the differential equation does not have any further measurement variables to be detected.
 22. A method as set forth in claim 18 characterized in that a weighted sum of the relative deviations from the target value is determined and the criterion is so selected
 23. A method as set forth in claim 18 characterized in that a plurality of criteria are predetermined, a fault event is associated with each criterion and, if a criterion is fulfilled, the associated fault event is diagnosed.
 24. A method as set forth in claim 17 characterized in that a model-based closed-loop control is used for the drive.
 25. A method as set forth in claim 24 characterized in that a non-linear state space model is selected as the model, wherein the non-linear closed-loop control is effected either by way of control-Lyapunov functions, by way of flatness-based closed-loop control methods with flatness-based precontrol, by way of integrator backstepping methods, by way of sliding mode methods or by way of predictive closed-loop control, wherein non-linear closed-loop control by way of control-Lyapunov functions is preferred.
 26. A method as set forth in claims 24 characterized in that the difference between the detected actual position profile of the displacer element and a predetermined target position profile of the displacer element is detected during a suction-pressure cycle and the difference of at least a part of the detected difference and the predetermined target position profile is used as the target value profile for the next suction-pressure cycle.
 27. A method as set forth in claim 17 characterized in that hydraulic parameters in the positive displacement pump are determined, for the hydraulic system a physical model is established with hydraulic parameters, the force exerted by the displacer element on the fluid in the metering chamber or the pressure in the metering chamber as well as the position of the displacer element is determined and at least one hydraulic parameter is calculated by means of an optimization calculation.
 28. A method as set forth in claim 27 characterized in that the density of the fluid in the metering chamber and/or the viscosity of the fluid in the metering chamber is determined as the hydraulic parameter.
 29. A method as set forth in claim 27 characterized in that the physical model is set up for the situation where the valve to the suction line is opened and the valve to the pressure line is closed and/or for the situation where the valve to the suction line is closed and the valve to the pressure line is opened, wherein if the physical model is set up both for the situation where the valve to the suction line is opened and the valve to the pressure line is closed and also for the situation where the valve to the suction line is closed and the valve to the pressure line is opened, the valve opening times are determined, and the physical model is selected in dependence on the result of determining the valve opening times.
 30. A method as set forth in claim 28 characterized in that after determination of the hydraulic parameter same and the physical model is used for determining the force exerted by the delivery fluid on the displacer element and the force determined in that way is used in a closed-loop control of the movement of the displacer element.
 31. A method as set forth in claim 18, characterized in that the positive displacement pump is an electromagnetically driven metering pump.
 32. A method as set forth in claim 19, characterized in that the positive displacement pump is an electromagnetically driven metering pump.
 33. A method as set forth in claim 18 characterized in that a model-based closed-loop control is used for the drive.
 34. A method as set forth in claim 19 characterized in that a model-based closed-loop control is used for the drive. 